Basic properties
Modulus: | \(6004\) | |
Conductor: | \(6004\) | sage: chi.conductor()
pari: znconreyconductor(g,chi)
|
Order: | \(78\) | sage: chi.multiplicative_order()
pari: charorder(g,chi)
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Real: | no | |
Primitive: | yes | sage: chi.is_primitive()
pari: #znconreyconductor(g,chi)==1
|
Minimal: | yes | |
Parity: | even | sage: chi.is_odd()
pari: zncharisodd(g,chi)
|
Galois orbit 6004.cy
\(\chi_{6004}(183,\cdot)\) \(\chi_{6004}(411,\cdot)\) \(\chi_{6004}(483,\cdot)\) \(\chi_{6004}(487,\cdot)\) \(\chi_{6004}(863,\cdot)\) \(\chi_{6004}(1699,\cdot)\) \(\chi_{6004}(1703,\cdot)\) \(\chi_{6004}(1927,\cdot)\) \(\chi_{6004}(2231,\cdot)\) \(\chi_{6004}(2311,\cdot)\) \(\chi_{6004}(2611,\cdot)\) \(\chi_{6004}(2767,\cdot)\) \(\chi_{6004}(3447,\cdot)\) \(\chi_{6004}(3527,\cdot)\) \(\chi_{6004}(3679,\cdot)\) \(\chi_{6004}(3755,\cdot)\) \(\chi_{6004}(3903,\cdot)\) \(\chi_{6004}(3907,\cdot)\) \(\chi_{6004}(4055,\cdot)\) \(\chi_{6004}(4435,\cdot)\) \(\chi_{6004}(4587,\cdot)\) \(\chi_{6004}(4891,\cdot)\) \(\chi_{6004}(4895,\cdot)\) \(\chi_{6004}(5579,\cdot)\)
Related number fields
Field of values: | $\Q(\zeta_{39})$ |
Fixed field: | Number field defined by a degree 78 polynomial |
Values on generators
\((3003,2529,3953)\) → \((-1,e\left(\frac{5}{6}\right),e\left(\frac{23}{39}\right))\)
First values
\(a\) | \(-1\) | \(1\) | \(3\) | \(5\) | \(7\) | \(9\) | \(11\) | \(13\) | \(15\) | \(17\) | \(21\) | \(23\) |
\( \chi_{ 6004 }(183, a) \) | \(1\) | \(1\) | \(e\left(\frac{12}{13}\right)\) | \(e\left(\frac{35}{39}\right)\) | \(e\left(\frac{59}{78}\right)\) | \(e\left(\frac{11}{13}\right)\) | \(e\left(\frac{47}{78}\right)\) | \(e\left(\frac{17}{78}\right)\) | \(e\left(\frac{32}{39}\right)\) | \(e\left(\frac{28}{39}\right)\) | \(e\left(\frac{53}{78}\right)\) | \(-1\) |